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Worried that Williams isn't a serious philosopher? Take a peek at his seminal theory, the Harmonic Constitution, which makes its debut late in his book.

What is it? In a nutshell, the Harmonic Constitution is a constitutional meta-theory combining three separation-of-powers theories into a unified proportional equation. It attempts to specify the correct proportions in a constitution of nine elements: democracy, aristocracy, monarchy, executive power, legislative power, judicial power, and the three matrices of geographic dispersion, the x,y,and z coordinates of the Cartesian grid. These nine elements are put into mutual balance by inserting them algebraically and geometrically into the ancient harmonic mean, thus the Harmonic Constitution. It is a theory posited by the American political philosopher M. C. Williams in his book, America On Trial. Williams contends that harmonic constitutionality achieves both maximum state power and maximum justice.

THE BASIC THEORY:

The Harmonic Constitution is a formula for political justice. Justice is always found in a mean of some kind, and political justice is always concerns who rules, how they rule, and where they rule. Hence, political Justice requires an amalgam of 3 separation-of-powers theories, one addressing each of these concerns, to wit: who gets to rule, (think Democracy/Monarchy/Aristocracy), how they rule, (executive/legislative/judicial power) and where they rule (federalism and fractal geometry) These three theories pre-date the Harmonic Constitution by hundreds and even thousands of years. The Harmonic Constitution merely combines them by applying a harmonic mean. This produces the Harmonic Constitution, a framework for weighing and analyzing all constitutions, thus a constitutional meta-theory.

Williams' theory combines three ‘separations’ of powers theories. The first of these concerns who rules. “Who gets to rule” is essentially the ancient separation of powers doctrine presented by Plato and Aristotle. The answer is a balance between the one, some and all, or Monarchy, Aristocracy, and Democracy. It is a 3-way separation of powers, often called the per-capita separation theory, or simply the ‘ancient’ separation of powers.

“How they rule” is essentially Montesquieu’s functional separation of powers, between executive, legislative and judicial exercise of power. This is also a three part separation of powers theory.

“Where they rule” is the federal question, namely, where do certain groups exercise certain functional powers, i.e. this government here, that one there, this above that, and those below these. This is a three-element separation, as each is arranged spatially on the x-y-z Cartesian grid. The question of where is geometrically solved by application of principles from Fractal Geometry. In brief, the constitution should be as fractal as possible, being made up entirely of smaller copies of itself, ad infinitum. Thus, the Harmonic Constitution purports to supply the ideal geometry of justice.

APPLYING THE HARMONIC MEAN

The Harmonic Constitution prescribes how these three separation theories, each subdivided into three components, “fit” together, i.e. how and in what proportion each of the sub-divisions or ‘elements’ interrelates with the others. It does this through application of the harmonic mean.
GEOMETRY OF THE HARMONIC MEAN

Geometrically speaking, the harmonic mean is obtained by cutting a line in two places such that the interior sections mirror the exterior. In the line segment A***B*C**D, the harmonic mean is realized if cuts are made at B and C, since the internal section B*C**D is proportional to the exterior sections, A**C****D. One is the other, flipped around and doubled.

The proportions are deduced through the following reasoning: Justice results from the government being balanced with the people, i.e. 50% of the power should be held by the people at large (the democratic element) and 50% by the government (aristocratic and Monarchic elements) Then, the Government itself should be a balance of the 3 functions, the Legislative, Executive, and Monarchic. The government’s three branches, and this is crucial, are not democratic. The government is completely made up of Aristocratic and Monarchic power, counterbalanced by the equal and opposite democratic element, the People. The Executive function is intrinsically Monarchic, and the Legislative and Judicial are Aristocratic (both being the rule of the few). When diagrammed geometrically, this turns out to be an instance of the harmonic mean, a geometric and algebraic formula mentioned by Euclid and Archimedes, among others. The Democratic Element is the people, and these have an equal power against the Government, influencing it through the elective and other processes.

SUB-THEORIES OF THE HARMONIC CONSTITUTION

Fractal Micro-Fedaralism. This sub-theory posits that all governments should be made up of smaller, identically formed governments, from the largest political unit down to the individual citizen. This purportedly is the most politically powerful constitutional arrangement. As the harmonic constitution is posited as the largest political unit, it follows that it must be federalized entirely into smaller harmonic constitutions, which are themselves likewise micro-federalized into still smaller harmonic constitutions, ad infinitum. This is known as fractal micro-federalism.

Constitutional Dialecticalism This sub-theory posits that the functional powers of legislation, execution, and adjudication continually fragment and recombine, ad infinitum. In an unbalanced constitution, they start as a whole, fragment into three, and then recombine, again and again. This process is arrested by the construction of a balanced harmonic constitution, whereupon the dialectical action is stayed by mutual counterbalance.